The Time-Energy Uncertainty Relation

The time energy uncertainty relation has been a controversial issue since the advent of quantum theory, with respect to appropriate formalisation, validity and possible meanings. A comprehensive account of the development of this subject up to the 1980s is provided by a combination of the reviews of Jammer (1974), Bauer and Mello (1978), and Busch (1990). More recent reviews are concerned with different specific aspects of the subject. The purpose of this chapter is to show that different types of time energy uncertainty relation can indeed be deduced in specific contexts, but that there is no unique universal relation that could stand on equal footing with the position-momentum uncertainty relation. To this end, we will survey the various formulations of a time energy uncertainty relation, with a brief assessment of their validity, and along the way we will indicate some new developments that emerged since the 1990s.Comment: 33 pages, Latex. This expanded version (prepared for the 2nd edition of "Time in quantum mechanics") contains minor corrections, new examples and pointers to some additional relevant literatur

Landscape and selection of vaccine epitopes in SARS-CoV-2

Background: Early in the pandemic, we designed a SARS-CoV-2 peptide vaccine containing epitope regions optimized for concurrent B cell, CD4+ T cell, and CD8+ T cell stimulation. The rationale for this design was to drive both humoral and cellular immunity with high specificity while avoiding undesired effects such as antibody-dependent enhancement (ADE). Methods: We explored the set of computationally predicted SARS-CoV-2 HLA-I and HLA-II ligands, examining protein source, concurrent human/murine coverage, and population coverage. Beyond MHC affinity, T cell vaccine candidates were further refined by predicted immunogenicity, sequence conservation, source protein abundance, and coverage of high frequency HLA alleles. B cell epitope regions were chosen from linear epitope mapping studies of convalescent patient serum, followed by filtering for surface accessibility, sequence conservation, spatial localization near functional domains of the spike glycoprotein, and avoidance of glycosylation sites. Results: From 58 initial candidates, three B cell epitope regions were identified. From 3730 (MHC-I) and 5045 (MHC-II) candidate ligands, 292 CD8+ and 284 CD4+ T cell epitopes were identified. By combining these B cell and T cell analyses, as well as a manufacturability heuristic, we proposed a set of 22 SARS-CoV-2 vaccine peptides for use in subsequent murine studies. We curated a dataset of ~ 1000 observed T cell epitopes from convalescent COVID-19 patients across eight studies, showing 8/15 recurrent epitope regions to overlap with at least one of our candidate peptides. Of the 22 candidate vaccine peptides, 16 (n = 10 T cell epitope optimized; n = 6 B cell epitope optimized) were manually selected to decrease their degree of sequence overlap and then synthesized. The immunogenicity of the synthesized vaccine peptides was validated using ELISpot and ELISA following murine vaccination. Strong T cell responses were observed in 7/10 T cell epitope optimized peptides following vaccination. Humoral responses were deficient, likely due to the unrestricted conformational space inhabited by linear vaccine peptides. Conclusions: Overall, we find our selection process and vaccine formulation to be appropriate for identifying T cell epitopes and eliciting T cell responses against those epitopes. Further studies are needed to optimize prediction and induction of B cell responses, as well as study the protective capacity of predicted T and B cell epitopes

Response of a Lake Michigan coastal lake to anthropogenic catchment disturbance

A paleolimnological investigation of post-European sediments in a Lake Michigan coastal lake was used to examine the response of Lower Herring Lake to anthropogenic impacts and its role as a processor of watershed inputs. We also compare the timing of this response with that of Lake Michigan to examine the role of marginal lakes as ‘early warning’ indicators of potential changes in the larger connected system and their role in buffering Lake Michigan against anthropogenic changes through biotic interactions and material trapping. Sediment geochemistry, siliceous microfossils and nutrient-related morphological changes in diatoms, identified three major trophic periods in the recent history of the lake. During deforestation and early settlement (pre-1845–1920), lake response to catchment disturbances results in localized increases in diatom abundances with minor changes in existing communities. In this early phase of disturbance, Lower Herring Lake acts as a sediment sink and a biological processor of nutrient inputs. During low-lake levels of the 1930s, the lake goes through a transitional period characterized by increased primary productivity and a major shift in diatom communities. Post-World War II (late 1940s–1989) anthropogenic disturbances push Lower Herring Lake to a new state and a permanent change in diatom community structure dominated by Cyclotella comensis . The dominance of planktonic summer diatom species associated with the deep chlorophyll maximum (DCM) is attributed to epilimnetic nutrient depletion. Declining Si:P ratios are inferred from increased sediment storage of biogenic silica and morphological changes in the silica content of Aulacoseira ambigua and Stephanodiscus niagarae . Beginning in the late 1940s, Lower Herring Lake functions as a biogeochemical processor of catchment inputs and a carbon, nutrient and silica sink. Microfossil response to increased nutrients and increased storage of biogenic silica in Lower Herring Lake and other regional embayments occur approximately 20–25 years earlier than in a nearby Lake Michigan site. Results from this study provide evidence for the role of marginal lakes and bays as nutrient buffering systems, delaying the impact of anthropogenic activities on the larger Lake Michigan system.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43091/1/10933_2004_Article_1688.pd